Struct DD

Implements extended-precision floating-point numbers which maintain 106 bits (approximately 30 decimal digits) of precision.

A DoubleDouble uses a representation containing two double-precision values. A number x is represented as a pair of doubles, x.hi and x.lo, such that the number represented by x is x.hi + x.lo, where

    |x.lo| <= 0.5*ulp(x.hi)

and ulp(y) means "unit in the last place of y". The basic arithmetic operations are implemented using convenient properties of IEEE-754 floating-point arithmetic.

The range of values which can be represented is the same as in IEEE-754. The precision of the representable numbers is twice as great as IEEE-754 double precision.

The correctness of the arithmetic algorithms relies on operations being performed with standard IEEE-754 double precision and rounding. This is the Java standard arithmetic model, but for performance reasons Java implementations are not constrained to using this standard by default. Some processors (notably the Intel Pentium architecture) perform floating point operations in (non-IEEE-754-standard) extended-precision. A JVM implementation may choose to use the non-standard extended-precision as its default arithmetic mode. To prevent this from happening, this code uses the Java strictfp modifier, which forces all operations to take place in the standard IEEE-754 rounding model.

The API provides both a set of value-oriented operations and a set of mutating operations. Value-oriented operations treat DoubleDouble values as immutable; operations on them return new objects carrying the result of the operation. This provides a simple and safe semantics for writing DoubleDouble expressions. However, there is a performance penalty for the object allocations required. The mutable interface updates object values in-place. It provides optimum memory performance, but requires care to ensure that aliasing errors are not created and constant values are not changed.

This implementation uses algorithms originally designed variously by Knuth, Kahan, Dekker, and Linnainmaa. Douglas Priest developed the first C implementation of these techniques. Other more recent C++ implementation are due to Keith M. Briggs and David Bailey et al.

References

• Priest, D., Algorithms for Arbitrary Precision Floating Point Arithmetic, in P. Kornerup and D. Matula, Eds., Proc. 10th Symposium on Computer Arithmetic, IEEE Computer Society Press, Los Alamitos, Calif., 1991.
• Yozo Hida, Xiaoye S. Li and David H. Bailey, Quad-Double Arithmetic: Algorithms, Implementation, and Application, manuscript, Oct 2000; Lawrence Berkeley National Laboratory Report BNL-46996.
• David Bailey, High Precision Software Directory; http://crd.lbl.gov/~dhbailey/mpdist/index.html

Implements

IComparable

IComparable<DD>

Inherited Members

object.Equals(object, object)

object.GetType()

object.ReferenceEquals(object, object)

Namespace: NetTopologySuite.Mathematics

Assembly: NetTopologySuite.dll

Syntax

[Serializable]
public struct DD : IComparable, IComparable<DD>

Constructors

DD(DD)

Creates a DD with a value equal to the argument

Declaration

public DD(DD dd)

Parameters

Type	Name	Description
DD	dd	The initial value

DD(double)

Creates a new DD with value x.

Declaration

public DD(double x)

Parameters

Type	Name	Description
double	x	The initial value

DD(double, double)

Creates a new DD with value (hi, lo).

Declaration

public DD(double hi, double lo)

Parameters

Type	Name	Description
double	hi	The high order component
double	lo	The low order component

DD(string)

Creates a new DD with value equal to the argument.

Declaration

public DD(string str)

Parameters

Type	Name	Description
string	str	The value to initialize by

Exceptions

Type	Condition
FormatException	if str is not a valid representation of a number

Fields

E

The value nearest to the constant e (the natural logarithm base).

Declaration

public static readonly DD E

Field Value

Type	Description
DD

Epsilon

The smallest representable relative difference between two DD values

Declaration

public static readonly double Epsilon

Field Value

Type	Description
double

NaN

A value representing the result of an operation which does not return a valid number.

Declaration

public static readonly DD NaN

Field Value

Type	Description
DD

PI

The value nearest to the constant Pi.

Declaration

public static readonly DD PI

Field Value

Type	Description
DD

PiHalf

The value nearest to the constant Pi / 2.

Declaration

public static readonly DD PiHalf

Field Value

Type	Description
DD

TwoPi

The value nearest to the constant 2 * Pi.

Declaration

public static readonly DD TwoPi

Field Value

Type	Description
DD

Properties

IsNegative

Gets a value indicating whether this object is negative or not

Declaration

public bool IsNegative { get; }

Property Value

Type	Description
bool

IsZero

Gets a value indicating whether this object is zero (0) or not

Declaration

public bool IsZero { get; }

Property Value

Type	Description
bool

Methods

Abs()

Returns the absolute value of this value.

Special cases:

• if this value is NaN, it is returned.

Declaration

public DD Abs()

Returns

Type	Description
DD	The absolute value of this value

Ceiling()

Returns the smallest (closest to negative infinity) value that is not less than the argument and is equal to a mathematical integer. Special cases:

• If this value is NaN, returns NaN.

Declaration

public DD Ceiling()

Returns

Type	Description
DD	The smallest (closest to negative infinity) value that is not less than the argument and is equal to a mathematical integer.

Clone()

Creates and returns a copy of this value.

Declaration

public object Clone()

Returns

Type	Description
object	A copy of this value

CompareTo(DD)

Compares two DoubleDouble objects numerically.

Declaration

public int CompareTo(DD other)

Parameters

Type	Name	Description
DD	other	An other DoubleDouble value

Returns

Type	Description
int	-1,0 or 1 depending on whether this value is less than, equal to or greater than the value of other

CompareTo(object)

Declaration

public int CompareTo(object o)

Parameters

Type	Name	Description
object	o

Returns

Type	Description
int

Copy(DD)

Creates a new DD with the value of the argument.

Declaration

public static DD Copy(DD dd)

Parameters

Type	Name	Description
DD	dd	The value to copy

Returns

Type	Description
DD	A copy of dd

Determinant(DD, DD, DD, DD)

Computes the determinant of the 2x2 matrix with the given entries.

Declaration

public static DD Determinant(DD x1, DD y1, DD x2, DD y2)

Parameters

Type	Name	Description
DD	x1	A matrix entry
DD	y1	A matrix entry
DD	x2	A matrix entry
DD	y2	A matrix entry

Returns

Type	Description
DD	The determinant of the matrix of values

Determinant(double, double, double, double)

Computes the determinant of the 2x2 matrix with the given entries.

Declaration

public static DD Determinant(double x1, double y1, double x2, double y2)

Parameters

Type	Name	Description
double	x1	A matrix entry
double	y1	A matrix entry
double	x2	A matrix entry
double	y2	A matrix entry

Returns

Type	Description
DD	The determinant of the matrix of values

Dump()

Dumps the components of this number to a string.

Declaration

public string Dump()

Returns

Type	Description
string	A string showing the components of the number

Equals(DD)

Tests whether this value is equal to another DoubleDouble value.

Declaration

public bool Equals(DD y)

Parameters

Type	Name	Description
DD	y	A DoubleDouble value

Returns

Type	Description
bool	true if this value == y.

Equals(object)

Declaration

public override bool Equals(object obj)

Parameters

Type	Name	Description
object	obj

Returns

Type	Description
bool

Overrides

ValueType.Equals(object)

Floor()

Returns the largest (closest to positive infinity) value that is not greater than the argument and is equal to a mathematical integer. Special cases:

• If this value is NaN, returns NaN.

Declaration

public DD Floor()

Returns

Type	Description
DD	The largest (closest to positive infinity) value that is not greater than the argument and is equal to a mathematical integer.

GetHashCode()

Declaration

public override int GetHashCode()

Returns

Type	Description
int

Overrides

ValueType.GetHashCode()

GreaterOrEqualThan(DD)

Tests whether this value is greater than or equals to another DoubleDouble value.

Declaration

public bool GreaterOrEqualThan(DD y)

Parameters

Type	Name	Description
DD	y	A DoubleDouble value

Returns

Type	Description
bool	true if this value >= y.

GreaterThan(DD)

Tests whether this value is greater than another DoubleDouble value.

Declaration

public bool GreaterThan(DD y)

Parameters

Type	Name	Description
DD	y	A DoubleDouble value

Returns

Type	Description
bool	true if this value > y.

IsInfinity(DD)

Checks if value is infinity.

Declaration

public static bool IsInfinity(DD value)

Parameters

Type	Name	Description
DD	value	A DoubleDouble value

Returns

Type	Description
bool	true if value is infinity.

IsNaN(DD)

Gets a value indicating whether this object is positive or not

Declaration

public static bool IsNaN(DD value)

Parameters

Type	Name	Description
DD	value

Returns

Type	Description
bool

IsPositive()

Gets a value indicating whether this object is positive or not

Declaration

public bool IsPositive()

Returns

Type	Description
bool

LessOrEqualThan(DD)

Tests whether this value is less than or equal to another DoubleDouble value.

Declaration

public bool LessOrEqualThan(DD y)

Parameters

Type	Name	Description
DD	y	A DoubleDouble

Returns

Type	Description
bool	true if this value is <= y

LessThan(DD)

Tests whether this value is less than another DoubleDouble value.

Declaration

public bool LessThan(DD y)

Parameters

Type	Name	Description
DD	y	A DoubleDouble value

Returns

Type	Description
bool	true if this value is < y

Max(DD)

Computes the maximum of this and another DD number.

Declaration

public DD Max(DD x)

Parameters

Type	Name	Description
DD	x	A DD number

Returns

Type	Description
DD	The maximum of the two numbers

Min(DD)

Computes the minimum of this and another DD number.

Declaration

public DD Min(DD x)

Parameters

Type	Name	Description
DD	x	A DD number

Returns

Type	Description
DD	The minimum of the two numbers

Parse(string)

Converts a string representation of a real number into a DoubleDouble value. The format accepted is similar to the standard Java real number syntax. It is defined by the following regular expression:

[+|-] {digit} [ . {digit} ] [ ( e | E ) [+|-] {digit}+

Declaration

public static DD Parse(string str)

Parameters

Type	Name	Description
string	str	The string to parse

Returns

Type	Description
DD	The value of the parsed number

Exceptions

Type	Condition
FormatException	Thrown if str is not a valid representation of a number

Pow(int)

Computes the value of this number raised to an integral power. Follows semantics of .Net Math.Pow as closely as possible.

Declaration

[Pure]
public DD Pow(int exp)

Parameters

Type	Name	Description
int	exp	The integer exponent

Returns

Type	Description
DD	x raised to the integral power exp

Reciprocal()

Returns a DD whose value is 1 / this.

Declaration

public DD Reciprocal()

Returns

Type	Description
DD	The reciprocal of this value

Rint()

Rounds this value to the nearest integer. The value is rounded to an integer by adding 1/2 and taking the floor of the result. Special cases:

• If this value is NaN, returns NaN.

Declaration

public DD Rint()

Returns

Type	Description
DD	This value rounded to the nearest integer

Signum()

Returns an integer indicating the sign of this value.

• if this value is > 0, returns 1
• if this value is < 0, returns -1
• if this value is = 0, returns 0
• if this value is NaN, returns 0

Declaration

public int Signum()

Returns

Type	Description
int	An integer indicating the sign of this value

Sqr()

Computes the square of this value.

Declaration

public DD Sqr()

Returns

Type	Description
DD	The square of this value

Sqr(double)

Computes the square of this value.

Declaration

public static DD Sqr(double x)

Parameters

Type	Name	Description
double	x

Returns

Type	Description
DD	The square of this value.

Sqrt()

Computes the positive square root of this value.

If the number is NaN or negative, NaN is returned.

Declaration

public DD Sqrt()

Returns

Type	Description
DD	If this is NaN or less than zero, the result is NaN.

Sqrt(double)

Computes the positive square root of a DoubleDouble value.

If the number is NaN or negative, NaN is returned.

Declaration

public static DD Sqrt(double x)

Parameters

Type	Name	Description
double	x	A numeric value

Returns

Type	Description
DD	the positive square root of this number. If the argument is NaN or less than zero, the result is NaN.

ToDoubleValue()

Converts this value to the nearest double number.

Declaration

public double ToDoubleValue()

Returns

Type	Description
double	The nearest double value

ToIntValue()

Converts this value to the nearest int value.

Declaration

public int ToIntValue()

Returns

Type	Description
int	The nearest int value

ToSciNotation()

Returns the string representation of this value in scientific notation.

Declaration

public string ToSciNotation()

Returns

Type	Description
string	The string representation in scientific notation

ToStandardNotation()

Returns the string representation of this value in standard notation.

Declaration

public string ToStandardNotation()

Returns

Type	Description
string	The string representation in standard notation

ToString()

Returns a string representation of this number, in either standard or scientific notation. If the magnitude of the number is in the range [ 10^-3, 10⁸ ] standard notation will be used. Otherwise, scientific notation will be used.

Declaration

public override string ToString()

Returns

Type	Description
string	A string representation of this number

Overrides

ValueType.ToString()

Truncate()

Returns the integer which is largest in absolute value and not further from zero than this value.

Special cases:

• If this value is NaN, returns NaN.

Declaration

public DD Truncate()

Returns

Type	Description
DD	The integer which is largest in absolute value and not further from zero than this value

ValueOf(double)

Converts the double argument to a DoubleDouble number.

Declaration

public static DD ValueOf(double x)

Parameters

Type	Name	Description
double	x	A numeric value

Returns

Type	Description
DD	The extended precision version of the value

ValueOf(string)

Converts the string argument to a DoubleDouble number.

Declaration

public static DD ValueOf(string str)

Parameters

Type	Name	Description
string	str	A string containing a representation of a numeric value

Returns

Type	Description
DD	The extended precision version of the value

Exceptions

Type	Condition
FormatException	Thrown if str is not a valid representation of a number

Operators

operator +(DD, DD)

Returns the sum of lhs and rhs.

Declaration

public static DD operator +(DD lhs, DD rhs)

Parameters

Type	Name	Description
DD	lhs	The left hand side
DD	rhs	The right hand side

Returns

Type	Description
DD	The sum of lhs and rhs

operator +(DD, double)

Returns the sum of lhs and rhs.

Declaration

public static DD operator +(DD lhs, double rhs)

Parameters

Type	Name	Description
DD	lhs	The left hand side
double	rhs	The right hand side

Returns

Type	Description
DD	The sum of lhs and rhs

operator /(DD, DD)

Divides lhs by rhs.

Declaration

public static DD operator /(DD lhs, DD rhs)

Parameters

Type	Name	Description
DD	lhs	A DoubleDouble numerator.
DD	rhs	A DoubleDouble divisor.

Returns

Type	Description
DD	The result of the division.

operator /(DD, double)

Divides lhs by rhs.

Declaration

public static DD operator /(DD lhs, double rhs)

Parameters

Type	Name	Description
DD	lhs	A DoubleDouble numerator.
double	rhs	A double divisor.

Returns

Type	Description
DD	The result of the division.

operator ==(DD, DD)

Equality operator for DoubleDouble values

Declaration

public static bool operator ==(DD lhs, DD rhs)

Parameters

Type	Name	Description
DD	lhs	A DoubleDouble value
DD	rhs	A DoubleDouble value

Returns

Type	Description
bool	true if lhs == rhs.

explicit operator DD(string)

Operator to parse a DoubleDouble from a string

Declaration

public static explicit operator DD(string val)

Parameters

Type	Name	Description
string	val	The DoubleDouble string

Returns

Type	Description
DD

implicit operator DD(double)

Operator to convert the double value to a DoubleDouble value.

Declaration

public static implicit operator DD(double val)

Parameters

Type	Name	Description
double	val	The DoubleDouble string

Returns

Type	Description
DD

operator !=(DD, DD)

Inequality operator for DoubleDouble values

Declaration

public static bool operator !=(DD rhs, DD lhs)

Parameters

Type	Name	Description
DD	rhs	A DoubleDouble value
DD	lhs	A DoubleDouble value

Returns

Type	Description
bool	true if lhs != rhs.

operator *(DD, DD)

Multiplies lhs by rhs.

Declaration

public static DD operator *(DD lhs, DD rhs)

Parameters

Type	Name	Description
DD	lhs	A DoubleDouble value.
DD	rhs	A DoubleDouble value.

Returns

Type	Description
DD	The result of the multiplication.

operator *(DD, double)

Multiplies lhs by rhs.

Declaration

public static DD operator *(DD lhs, double rhs)

Parameters

Type	Name	Description
DD	lhs	A DoubleDouble value.
double	rhs	A double value.

Returns

Type	Description
DD	The result of the multiplication.

operator -(DD, DD)

Returns the difference of lhs and rhs.

Declaration

public static DD operator -(DD lhs, DD rhs)

Parameters

Type	Name	Description
DD	lhs	The left hand side
DD	rhs	The right hand side

Returns

Type	Description
DD	The difference of lhs and rhs

operator -(DD, double)

Returns the difference of lhs and rhs.

Declaration

public static DD operator -(DD lhs, double rhs)

Parameters

Type	Name	Description
DD	lhs	The left hand side
double	rhs	The right hand side

Returns

Type	Description
DD	The difference of lhs and rhs

operator -(DD)

Subtracts the argument from the value of this.

Declaration

public static DD operator -(DD val)

Parameters

Type	Name	Description
DD	val	The subtrahend

Returns

Type	Description
DD	The result of this - y

Implements

IComparable

IComparable<T>